Problem: Rewrite as a simplified fraction. ${0.6\overline{19} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 619.1919...\\ 10x &= 6.1919...\end{align*}}$ Subtracting the two equations, we have: ${990x = 613}$ ${x = \dfrac{613}{990}} $